High speeds due to gravitaional forces

Main Question or Discussion Point

Is it possible for a massive body to accelerate an object, say a 1kg mass, to a speed which is light speed or near light speed? What mass would this body have to be, and how far away would the 1 kg mass have to be?

By definition, any time you're asking about getting close to the speed of light---thats relativistic. Also, note that you can never reach or exceed the speed of light.

You can do a newtonian approximation to your question, the projectile motion equation for velocity is
[tex]V_f^2 = V_i^2 + 2ad[/tex]
for final velocity V_f, initial velocity V_i, acceleration a, and distance d.
Do you know how to find the acceleration between two massive point particles?

The maximum velocity you can get for a given body is the same as the escape velocity for that body. It will depend on the radius and mass of the massive body only. You can find it from energy conservation. You start with your 1 kg mass very far away (PE=0, KE=0) and then you approach the body till you reach the surface.

The maximum velocity you can get for a given body is the same as the escape velocity for that body. It will depend on the radius and mass of the massive body only. You can find it from energy conservation. You start with your 1 kg mass very far away (PE=0, KE=0) and then you approach the body till you reach the surface.

This isn't true. Fire a projectile at the Sun at a speed greater than the escape velocity of the Sun (about 600 km/s) and you'll of course accelerate to a speed faster than the escape velocity. The only issue is if you miss the Sun, it will fly off and never become captured by the Sun. However, if you aim right at it, you'll accelerate to quite a high speed!

And that's quite an extreme case, simply fire projectile with a kinetic energy greater than the potential energy of the object at whatever radii it is at and you'll achieve a speed greater than the escape velocity.